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Causal Structure Discovery (CSD) is the problem of identifying causal relationships from large quantities of data through computational methods. With the limited ability of traditional association-based computational methods to discover causal relationships, CSD methodologies are gaining popularity. The goal of the study was to systematically examine whether (i) CSD methods can discover the known causal relationships from observational clinical data and (ii) to offer guidance to accurately discover known causal relationships. We used Alzheimer's disease (AD), a complex progressive disease, as a model because the well-established evidence provides a "gold-standard" causal graph for evaluation. We evaluated two CSD methods, Fast Causal Inference (FCI) and Fast Greedy Equivalence Search (FGES) in their ability to discover this structure from data collected by the Alzheimer's Disease Neuroimaging Initiative (ADNI). We used structural equation models (which is not designed for CSD) as control. We applied these methods under three scenarios defined by increasing amounts of background knowledge provided to the methods. The methods were evaluated by comparing the resulting causal relationships with the "gold standard" graph that was constructed from literature. Dedicated CSD methods managed to discover graphs that nearly coincided with the gold standard. For best results, CSD algorithms should be used with longitudinal data providing as much prior knowledge as possible.